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Multispectral Sensing
Published in S. Sitharama Iyengar, Richard R. Brooks, Distributed Sensor Networks, 2016
Besides the issue of boundary conditions, it is well-known that the color image restoration problem is very ill-conditioned, and restoration algorithms will be extremely sensitive to noise. In Ref. [30], the regularized least squares filters [31,32] are used to alleviate the restoration problem. It is shown that the resulting regularized least squares problem can be solved efficiently by using DCTs. In the regularized least squares formulation, regularization parameters are introduced to control degree of bias of the solution. The generalized cross-validation function is also used to obtain estimates of these regularization parameters, and then to restore high-quality color images. Numerical examples are given in Ref. [30] to illustrate the effectiveness of the proposed methods over other restoration methods.
A multi-sensor fusion-based prognostic model for systems with partially observable failure modes
Published in IISE Transactions, 2023
This subsection is devoted to investigating the performance of the proposed method on failure mode identification and the influence of kernel selection. In particular, we compare the proposed HLapRLS with the traditional Laplacian Regularized Least Squares (LapRLS), the traditional Regularized Least Squares (RLS), and a revised RLS, denoted by HRLS. The former two algorithms have been discussed in Belkin et al. (2006). The HRLS is formulated the same as the proposed HLapRLS with All these methods employ a Gaussian kernel. Furthermore, we investigate three kernels for the proposed HLapRLS, i.e., the Gaussian kernel, the linear kernel, and the polynomial kernel. The tuning parameters of each algorithm are determined using the selection procedures in Section 3. We employ the geometric mean (g-mean) to evaluate the performance. It is defined as follows:
Least squares formulation for ill-posed inverse problems and applications
Published in Applicable Analysis, 2022
Eric Chung, Kazufumi Ito, Masahiro Yamamoto
In order to have an effective solution to the regularized least squares formulation (4) it is essential to select the regularization parameter . One can use a balancing principle [3, 5] for the selection of the regularization parameter . By the Bayes inference, we have where we assume that and have the Gamma distribution with shape parameters and , i.e. . Then, the necessary optimality condition of any minimizer (MAP estimate) of this functional is given by where . Thus, in terms of α, we have Equivalently, we obtain the balance principle Specifically, if are sufficiently small, it reduces to where we assume . We refer [3, 4] for the convergence analysis and an efficient iterative method to find that satisfies (10).
RBF level-set based fully-nonlinear fluorescence photoacoustic pharmacokinetic tomography
Published in Inverse Problems in Science and Engineering, 2021
Omprakash Gottam, Naren Naik, Prabodh Kumar Pandey, Sanjay Gambhir
Consider the Tikhonov regularized least squares problem The gradient of this cost function is given by The derivatives of the measurement residuals at various time instants with respect to is given as Denoting , where the , , are defined in Equation (29), we can write where , where the , , are defined in Equation (20).